On the Riemannian geometry of Seiberg–Witten moduli spaces

We construct a natural L²$L^2$-metric on the perturbed Seiberg–Witten moduli spaces _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ of a compact 4-manifold M$M$, and we study the resulting Riemannian geometry of _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$. We derive a formula which expresses the sectional curvature of _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ in terms of the Green operators of the deformation complex of the Seiberg–Witten equations. In case M$M$ is simply connected, we construct a Riemannian metric on the Seiberg–Witten principal U(1)$U\left(1\right)$ bundle P→_Mμ+$\mathfrak{P}\to {\mathfrak{M}}_{{\mu }^{+}}$ such that the bundle projection becomes a Riemannian submersion. On a Kähler surface M$M$, the L²$L^2$-metric on _Mμ+${\mathfrak{M}}_{{\mu }^{+}}$ coincides with the natural Kähler metric on moduli spaces of vortices.     

First-principles materials design of CuInSe2-based high-efficiency photovoltaic solar cells

Based on ab initio   electronic structure calculations by self-interaction-corrected local-density-approximation (SIC-LDA) with the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA), we propose a materials design for high efficiency photovoltaic solar cells (PVSCs). It is shown that (i) the concentration dependence of the mixing energy of CuIn_1−xGa_xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Ga}}_x{\mathrm{Se}}_2$ shows upward convexity, thus this system favors phase separation. Due to the type II band alignment between CuInSe₂${\mathrm{CuInSe}}_2$ and CuGaSe₂${\mathrm{CuGaSe}}_2$, efficient electron–hole separation is realized in decomposed phase of this system. (ii) CuIn_1−xZn_0.5xSn_0.5xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Zn}}_{0.5x}{\mathrm{Sn}}_{0.5x}{\mathrm{Se}}_2$ has a direct band gap and no impurity state appears in the gap. Therefore, cost reduction is possible by using Zn and Sn instead of In. (iii) n-type CuAl_1−xSn_xS₂${\mathrm{CuAl}}_{1-x}{\mathrm{Sn}}_x{\mathrm{S}}_2$ and p-type Cu_1−xV_CuxAlS₂${\mathrm{Cu}}_{1-x}{\mathrm{V}}_{\mathrm{Cu}x}{\mathrm{AlS}}_2$ have negative activation energy for doped impurities and are expected to be low-resistive transparent conducting sulfides, which should be useful for CuInSe₂${\mathrm{CuInSe}}_2$-based PVSCs.     

First search for double β decay of dysprosium

A search for double β decay of dysprosium was realized for the first time with the help of an ultra-low background HP Ge γ detector. After 2512 h of data taking with a 322 g sample of dysprosium oxide limits on double beta processes in ¹⁵⁶Dy and ¹⁵⁸Dy have been established on the level of T_1/2?¹⁰¹⁴–¹⁰¹⁶ yr$T_{1/2}?{10}^{14}\text{–}{10}^{16}\text{yr}$. Possible resonant double electron captures in ¹⁵⁶Dy and ¹⁵⁸Dy were restricted on a similar level. As a by-product of the experiment we have measured the radioactive contamination of the Dy₂O₃ sample and set limits on the α   decay of dysprosium isotopes to the excited levels of daughter nuclei as T_1/2?¹⁰¹⁵–¹⁰¹⁷ yr$T_{1/2}?{10}^{15}\text{–}{10}^{17}\text{yr}$.     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

The antiferromagnetic Ising model for a bilayer Bethe lattice

The totally antiferromagnetic Ising model is analyzed on a bilayer Bethe lattice in detail by studying the order-parameters, response functions, i.e. susceptibility and specific heat, and free energy by using the recursion relations in a pairwise approach. The ground state phase diagrams of the model are also obtained on the (_J2/|_J1|,_J3/q|_J1|)$(J_2/|J_1|,J_3/q|J_1|)$ plane for given values of H/q|_J1|$H/q\left|J_1\right|$ and on the (H/q|_J1|,_J3/q|_J1|)$(H/q|J_1|,J_3/q|J_1|)$ plane for given _J2/|_J1|$J_2/\left|J_1\right|$. As a result, we have obtained the temperature-dependent phase diagrams for various values of the coordination number q   on the (_J3/|_J1|,kT/|_J1|)$(J_3/|J_1|,\mathit{kT}/|J_1|)$ and (H/|_J1|,kT/|_J1|)$(H/|J_1|,\mathit{kT}/|J_1|)$ planes for given values of the rest of the system parameters.     

Phase diagrams of a spin-1 Ising superlattice

The three-dimensional spin-1 Ising superlattice consisting of two different ferromagnetic materials with two different crystal fields _Δ1${\Delta }_1$ and _Δ2${\Delta }_2$ is considered in the mean field approximation. The phase diagrams are considered in the (t,_d2$t,d_2$) plane for different ranges of variation of _d1(t=T/J,_d1=_Δ1/J$d_1(t=T/J,d_1={\Delta }_1/J$, _d2=_Δ2/J$d_2={\Delta }_2/J$ are the reduced temperature and crystal fields respectively). The phase diagrams exhibit a variety of multicritical points and reentrant and double reentrant behaviours. They are found to depend qualitatively and/or quantitatively on the thicknesses of the materials in a supercell. This has direct consequences on the nature of the magnetic states of superlattices with different thicknesses.     

Properties of fermion mixings in intersecting D-brane models

We consider the Yukawa couplings for quarks and leptons in the context of Pati–Salam model using intersecting D-brane models where the Yukawa coupling matrices are rank one in a simple choice of family replication. The CKM mixings can be explained by perturbing the rank 1 matrix using higher order terms involving new Higgs fields available in the model. We show that the near bi-large neutrino mixing angles can be naturally explained, choosing the light neutrino mass matrix to be type II seesaw dominant. The predicted value of U_e3$U_{e3}$ is in the range ?0.05–0.15$?0.05\text{–}0.15$. In the quark sector, V_cb$V_{cb}$ is naturally close to the strange/bottom quark mass ratio and we obtain an approximate relation V_ubV_cb?(ms/mb)²V_us$V_{ub}{V}_{cb}?{(m_s/m_b)}^2{V}_{us}$. The geometrical interpretations of the neutrino mixings are also discussed.     

Surface magnetic phase transitions in films

Using a simple Landau model, we discuss the different possibilities of generating magnetic effects at a second-order transition for films. Varying the sample size d$d$ and/or surface coupling γ$\gamma$ one can decrease or increase substantially the surface critical temperature _Ts$T_{\mathrm{s}}$ and the saturation magnetization _Ms$M_{\mathrm{s}}$. In the case of γ>0$\gamma >0$, _Ms$M_{\mathrm{s}}$ and _Ts$T_{\mathrm{s}}$ decrease from the bulk values as the film thickness is reduced. These theoretical results are in nice agreement with the experimental data on superconducting _MgB2${\mathrm{MgB}}_2$ thin films. By contrast, for γ<0$\gamma <0$, an enhancement of both quantities is expected. This extraordinary transition has rarely been observed experimentally and, usually, the situation is far from being clear. We analyze a new experiment on _NiFe2O4${\mathrm{NiFe}}_2{\mathrm{O}}_4$ ultra-thin films, where a very strong enhancement of the saturation magnetization is observed.     

Shot noise in HTc superconductor quantum point contact system

We study the electrical transport properties of a quantum point contact between a lead and a high Tc superconductor. For this, we use the Hamiltonian approach and non-equilibrium Green functions of the system. The electrical current and the shot noise are calculated with this formalism. We consider d_x²−y²${\mathrm{d}}_{x^2-y^2}$, d_xy${\mathrm{d}}_{\mathit{xy}}$, d_x²−y²+is${\mathrm{d}}_{x^2-y^2}+\mathrm{is}$ and d_xy+is${\mathrm{d}}_{\mathit{xy}}+\mathrm{is}$ symmetries for the pair potential. Also we explore the s₊₋${\mathrm{s}}_{+-}$ and s₊₊${\mathrm{s}}_{++}$ symmetries describing the behavior of the ferropnictides superconductors. We found that for d_xy${\mathrm{d}}_{\mathit{xy}}$ symmetry there is not a zero bias conductance peak and for d+is$\mathrm{d}+\mathrm{is}$ symmetries there is a displacement of the transport properties. From shot noise and current, the Fano factor is calculated and we found that it takes values of effective charge between e and 2e  , this is explained by the diffraction of quasiparticles in the contact. For the s₊₋${\mathrm{s}}_{+-}$ and s₊₊${\mathrm{s}}_{++}$ symmetries the results show that the electrical current and the shot noise depend on the mixing coefficient, furthermore, the effective electric charge can take values between 0 and 2e, in contrast with the results obtained for s wave superconductors.     

Fermi matrix element with isospin breaking

Prompted by the level of accuracy now being achieved in tests of the unitarity of the CKM matrix, we consider the possible modification of the Fermi matrix element for the β  -decay of a neutron, including possible in-medium and isospin violating corrections. While the nuclear modifications lead to very small corrections once the Behrends–Sirlin–Ademollo–Gatto theorem is respected, the effect of the u−d$u-d$ mass difference on the conclusion concerning V_ud$V_{ud}$ is no longer insignificant. Indeed, we suggest that the correction to the value of |V_ud|²+|V_us|²+|V_ub|²${|V_{ud}|}^2+{|V_{us}|}^2+{|V_{ub}|}^2$ is at the level of ¹⁰⁻⁴${10}^{-4}$.     

On partition function and Weyl anomaly of conformal higher-spin fields

We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s   fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2$s=2$) partition function. We compute the corresponding spin s   Weyl anomaly coefficients _as${\mathrm{a}}_s$ and _cs${\mathrm{c}}_s$. Our result for _as${\mathrm{a}}_s$ reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S⁴$S^4$ to a ratio of known partition functions of massless higher-spin field in AdS₅ with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic _as${\mathrm{a}}_s$ coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case.     

About the fastest growth of the Order Parameter in models of percolation

The growth of the average size 〈_smax〉$〈s_{max}〉$ of the largest component at the percolation threshold _pc(N)$p_c\left(N\right)$ on a graph of size N$N$ has been defined as 〈_smax(_pc(N),N)〉∼N^χ$〈s_{max}(p_c\left(N\right),N)〉\sim N^{\chi }$. Here we argue that the precise value of the ‘growth exponent’ χ$\chi$ indicates the nature of percolation transition; χ<1$\chi <1$ or χ=1$\chi =1$ determines if the transition is continuous or discontinuous. We show that a related exponent η=1−χ$\eta =1-\chi$ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by the weighted average of these distributions and for the distribution of the maximal jump in the Order Parameter.